Stationary distribution of a multi-server vacation queue with constant impatient times

Sakuma, Yutaka; Inoie, Atsushi

doi:10.1016/j.orl.2012.03.006

Cited by 4 publications

(2 citation statements)

References 14 publications

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“…Yechiali [15] considered an M/M/c system which as a whole suffers occasionally a disastrous breakdown, upon which all present customers (waiting and served) are cleared from the system and lost. Stationary distribution of a multiserver vacation queue with constant impatient times is studied by Sakuma and Inoie [16]. Chen et al [17] studied M/M/m/k queue with preemptive resume and impatience of the prioritised customers and derived the queue length distraction in stationary state and performance measures using the method of matrix analysis.…”

Section: Advances In Operations Researchmentioning

confidence: 99%

Phase-Type Arrivals and Impatient Customers in Multiserver Queue with Multiple Working Vacations

Goswami

Selvaraju

2016

Advances in Operations Research

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We consider a PH/M/c queue with multiple working vacations where the customers waiting in queue for service are impatient. The working vacation policy is the one in which the servers serve at a lower rate during the vacation period rather than completely ceasing the service. Customer’s impatience is due to its arrival during the period where all the servers are in working vacations and the arriving customer has to join the queue. We formulate the system as a nonhomogeneous quasi-birth-death process and use finite truncation method to find the stationary probability vector. Various performance measures like the average number of busy servers in the system during a vacation as well as during a nonvacation period, server availability, blocking probability, and average number of lost customers are given. Numerical examples are provided to illustrate the effects of various parameters and interarrival distributions on system performance.

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Section: Advances In Operations Researchmentioning

confidence: 99%

Phase-Type Arrivals and Impatient Customers in Multiserver Queue with Multiple Working Vacations

Goswami

Selvaraju

2016

Advances in Operations Research

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show abstract

“…The authors derived some performance measures and the stochastic decomposition. Sakuma and Inoie [2012] analysed the M/M/c + D queue with multiple vacation exponentially distributed, where customers are impatient only when all servers are unavailable. He derives the stationary distribution of the system using the matrix-analytic method.…”

Section: Introductionmentioning

confidence: 99%